teaching, math, teaching math

Scientific Knowledge for Teaching

[R]esearchers have argued that teachers’ learning should not be limited to practical classroom strategies. The teacher who understands the psychological principles undergirding the recommended strategies will presumably find them more sensible and will see ties between seemingly disparate strategies. Perhaps most important, that teacher will also generalize strategies to novel situations. Teachers need what might be called a mental model of the learner: knowledge of children’s cognitive, emotional, and motivational makeup.

So teachers will benefit from knowing some things about how students learn. But what exactly, would teachers benefit from knowing? Willingham distinguishes between three types of knowledge in science: empirical observations, theoretical statements, and epistemic assumptions. The whole paper is worth a read, but I’d like to focus on one element of his argument that was particularly compelling for me. My paraphrase:

Teachers can benefit from bottom-up knowledge that is built on concrete observations, whether those observations are from research or their own practice. Top-down knowledge that begins with broad theories or generalizations about learning are likely to be less useful.

If teachers focus on bottom-up knowledge, they have the opportunity to buttress their everyday observations in classrooms with additional examples from research into how humans learn, building a rich and experience-based model of how their students learn. This type of knowledge is more likely to be humble; learning is fickle, and a certain practice may work in one context but not in another. Teachers are always learning, observing, and developing a more robust understanding of learning. If teachers focus on top-down knowledge, they come to their experience with broad statements about how students learn that can be adapted to justify a range of practices, separate from any evidence that they are effective for students. Willingham writes:

A statement like “learning is social” could be taken to mean “children learn best in social situations,” which is actually a very different statement–it is a statement about how children behave. But confusing it with “learning is social” could easily lead to thinking that because group discussion is more social than teacher instruction, it is a settled matter that it is more effective for learning, whereas the empirical reality is far more complicated.

In short, top-down knowledge about teaching can be twisted to support a range of ideas, and distances itself from everyday experience. Two examples of where I see this happen:

Cognitive Load Theory

From a top-down perspective, cognitive load theory is a theory that, in problem solving situations, students’ working memory becomes overloaded, preventing them from learning. This statement could be used to justify any number of teaching practices, and to foreclose entirely any problem-oriented learning. But from a bottom-up perspective, cognitive load theory is a set of experiments in which, under certain conditions, students become overwhelmed by the demands of problem-solving and unable to learn from that experience. This perspective, while only subtly different, sets teachers up to incorporate that knowledge with their own experiences and to approach new situations with some humility — cognitive load theory doesn’t prescribe a course of action, but offers evidence for a practice that seems not to work in some contexts.

Constructivism

From a top-down perspective, constructivism is the perspective that learners actively construct new knowledge. It is often used to support inquiry-oriented approaches to learning, with the justification that if learners are to construct their own knowledge, they need to be active participants in that process. From a bottom-up perspective, constructivism is the recognition that what students learn depends on what they already know, and incorporates both teachers’ experience and research into how prior knowledge can have a large influence on future learning.

In both cases, the shift is away from prescriptive theories that try to make broad statements about best practice, and toward a focus on building a broad base of knowledge for teachers to draw from in their instructional decisions. Rather than coming into the classroom with preconceptions about what learning must look like, a bottom-up approach emphasizes concrete experience, the importance of context, and humility.

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4 thoughts on “Scientific Knowledge for Teaching”

I love this observation about how theories are used in many different directions. I still believe teachers should use those theories because I want teachers to have a coherent system of teaching and if they are coherent I’m open to them having different systems. The theory can help even teachers that I disagree with to have a better aligned set of expectations from their students.

Interesting. I can definitely see the value both ways. But what about the value of a belief system that helps teachers incorporate new knowledge and change their minds as necessary? I know I’ve changed my mind about most aspects of my teaching, often more than once.

I change my mind a lot about things. It does not prevent me from holding a firm believe in my way in any given day. Maybe it’s a cultural thing but I can’t change my mind if I don’t have an idea to start with and get confused about. I see a problem today with teachers trying to mix and match too many things that don’t have a connecting thread between them and it makes classes be harder to manage and to take to great places.